The belief that the Golden Section has, through the ages, been purposely built into buildings, paintings, or sonatas, or that it is somehow part of the world or of our brains is one that has sprung up fairly recently.
The idea that a rectangle with dimensions Phi (aka Golden Section) and 1 (or, equivalently, 1 and Phi - 1) is the one that is aesthetically most pleasing seems to have gotten a start in the 1860s, though too many authors repeat this as if it were part of the wisdom of the ages. Back then, one Gustav Fechner presented subjects with ten rectangles and asked them which they thought was the nicest. The rectangles varied from a square to one whose sides had the ratio of 2 to 5 -- that is, with aspect ratios from 1 to .4. The three rectangles in the middle, those with aspect ratios .57, .62, and .67, were chosen by 76% of the subjects.
Well, of course. Squares are dull, long flat rectangles look as if they had been stepped on, and tall skinny rectangles make us nervous-they look as if they may fall over any minute-so naturally something in the middle gets picked. But the golden section has nothing to do with it. Further studies have shown that golden rectangles are in fact not the prettiest. There is now (at least there was when this was written) a Web poll on the subject, which may be found at http://homepage.esoterica.pt/~madureir, that has rectangles with width 54 and heights 65, 68, 72, 77, 81, 87, 96, 108. The sixth is close to a golden rectangle, but it has been picked as the most pleasing rectangle by only 12% of the 1501 respondents to the poll. The 54-by-72 rectangle is the clear winner, with 30% of the votes. (The percentages of respondents choosing each of the eight rectangles are, respectively, 9, 3, 30, 16, 19, 12, 5, 8.) If you measure books, a handy source of rectangles, you will find that almost none has dimensions that come close to those of a golden rectangle. A golden-rectangle book looks too tall and skinny.
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